On the Neumann problem for the Sturm-Liouville equation with Cantor-type self-similar weight

DOI10.1007/s10688-013-0033-9zbMath1310.34038OpenAlexW2106370538MaRDI QIDQ482569

I. A. Sheipak, A. A. Vladimirov

Publication date: 5 January 2015

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10688-013-0033-9

zbMATH Keywords

Neumann boundary conditionsSturm-Liouville problemself-similar weightspectral periodicitythird-type boundary conditions

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

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Cites Work

• Asymptotics of the eigenvalues of the Sturm-Liouville problem with discrete self-similar weight
• Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
• Strongly definitizable linear pencils in Hilbert space
• Indefinite Sturm-Liouville problem for some classes of self-similar singular weights
• On the construction and some properties of self-similar functions in the spaces \(L_{p}[0, 1\)]
• Oscillation theorems for Sturm-Liouville problems with distribution potentials
• Asymptotics of eigenvalues in a problem of high even order with discrete self-similar weight
• Self-similar functions in $ L_2\lbrack0,1\rbrack$ and the Sturm-Liouville problem with a singular indefinite weight
• On A Set Of Transformations of Gaussian Random Functions
• On the oscillation theory of the Sturm-Liouville problem with singular coefficients
• On a Spectral Problem Related to Self-Similar Measures
• Spectral Asymptotics, Renewal Theorem, and the Berry Conjecture for a Class of Fractals
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